This must be a question with no good answer.
My understanding is that being too immunocompromised for a vaccine happens in two different ways:
1) the vaccine contains live virus and so there's danger that the weak immune system couldn't fight this off
2) the vaccine isn't live, so it's not dangerous on its own, but the immune system is too weak to recognize it, so it doesn't build any immunity to the real thing. (One doctor I was talking to said the mRNA ones should be good here, because your own body produces so much of the lookalikes that even a weak immune system should notice it - and then you're much better prepared to fight the real thing off faster.)
Only the first is immediately dangerous, so the standard seems to be to just stay away from those.
I'm not sure if much is commonly done for the second, in terms of looking for response, but you can get tests for measles antibodies and such, so that would probably be how?